There are many benefits to using the golden ratio in logos:

Visually appealing: The golden ratio makes your logo look balanced and harmonious. This makes your logo easier to remember and adopt by viewers.
Timeless: The golden ratio has been used for centuries and is a ratio that never goes out of style. Therefore, a logo designed using the golden ratio will remain attractive for many years.
Meaningful: The golden ratio is associated with nature and perfection. Therefore, a logo designed using the golden ratio can add a sense of reliability and quality to your product or service.
Universal: The golden ratio is considered aesthetically pleasing in many cultures around the world. Therefore, a logo designed using the golden ratio can appeal to people from different cultures.
For more information: What is the Golden Ratio and How to Use It in Design